Hierarchical tree-model of 2D-turbulence

Abstract

A model system akin to 2D-turbulence has been constructed as a hierarchical tree of vortices of different sizes. In contrast to cascade models, the number of degrees of freedom grows with wave number, as in real turbulence: modelling comes in only in the connections and interactions of the vortices. The functional form of the vortices are taken from a discrete, hierarchical basis, well localized in both real-space and Fourier-space. The vortices are connected along the back-bone of the tree, but not horizontally on a given level. The behaviour including neighbour and next-neighbour interactions in scale is compared. The inertial forces conserve both energy and enstrophy, and exhibits the forward cascade of enstrophy. Statistical properties of the cascade are investigated, both integral and local. The energy spectrum and other quantites do not seem to depend significantly on the initial conditions nor on the details of the driving forces.